CONDITIONS FOR EXISTENCE AND UNIQUENESS OF THE INVERSE FIRST-PASSAGE TIME PROBLEM APPLICABLE FOR LÉVY PROCESSES AND DIFFUSIONS

被引：0

作者：

Klump, Alexander ^{[1
]}

Savov, Mladen ^{[2
]}

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, Sofia, Bulgaria

[2] Sofia Univ St Kliment Ohridski, Fac Math & Informat, Sofia, Bulgaria

来源：

ANNALS OF APPLIED PROBABILITY | 2025年 / 35卷 / 03期

关键词：

stochastic process; Markov process; L & eacute; vy process; diffusion; Inverse first-passage time problem; FREE-BOUNDARY;

D O I：

10.1214/25-AAP2157

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

For areal-valued stochastic process (X-t)(t>0) we establish conditions under which the inverse first-passage time problem has a solution for any random variable xi> 0. For Markov processes we give additional conditions under which the solutions are unique and solutions corresponding to ordered initial states fulfill a comparison principle. As examples we show that these conditions include L & eacute;vy processes with infinite activity or unbounded variation and diffusions on an interval with appropriate behavior at the boundaries. Our methods are based on the techniques used in the case of Brownian motion and rely on discrete approximations of solutions via Gamma-convergence from (Theory Probab. Appl. 25 (1980) 362-366) and (Ann. Appl. Probab. 21 (2011) 1663-1693) combined with stochastic ordering arguments adapted from (Theory Probab. Appl. 67 (2023) 570-592).

引用

页码：1791 / 1827

页数：37

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